Given points A2 4 and B5 1 in a rectangular coordinate syste

Given points A(2, 4) and B(-5, 1) in a rectangular coordinate system, find a formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector ell of line segment AB.

Solution

A(2,4)    and   B(-5,1)

Slope= (1-4)/(-5-2)=3/7

Therefore slope of required line=-7/3

And point is (x,y) which is on perpendicular bisetor of AB

So we have to find the mid point of AB

((x₁+x₂)/2 , (y₁+y₂)/2)   =   ((2-5)/2,(4+1)/2)   = (-1.5,2.5 )

Therefore P(-1.5,2.5)

We will use the point slope form which is

y-2.5= -7/3(x+1.5)

3y-7.5= -7x-10.5

3y= -7x -3

y= -7x/3    -1